The circle on `SS^'` as diameter intersects the ellipse in real points then its eccentricity

Let S and S' be two foci of the ellipse (x^(2))/(a^(3))+(y^(2))/(b^(2))=1. If a circle described on SS' as diameter intersects the ellipse at real and distinct points,then the eccentricity e of the ellipse satisfies c=(1)/(sqrt(2))( b) e in((1)/(sqrt(2)),1)e in(0,(1)/(sqrt(2)))(d) none of these

Intersection of Ellipse with Circle

An ellips inscribed in a semi-cicle touches the cicular are at two distinct points and also touches the bounding diameter. Its major axis is parallel to the bounding diameter. When the ellipse has the maximum passible area, its eccentricity is -

If a circle intercepts the ellipse at four points, show that the sum of the eccentric angles of these points is an even multiple of pi

A circle described with minor axis of an ellipse as a diameter. If the foci lie on the circle, the eccentricity of the ellipse is

A circle is described with minor axis of an ellipse as a diameter. If the foci lie on the circle, the eccentricity of the ellipse is

A variable tangent to the circle x^(2)+y^(2)=1 intersects the ellipse (x^(2))/(4)+(y^(2))/(2)=1 at point P and Q. The lous of the point of the intersection of tangents to the ellipse at P and Q is another ellipse. Then find its eccentricity.